Question
Identify the greater number, if possible: $100^2$ and $2^{100}$
✓
Answer
In order to find the greater number in these two numbers, we should expand and find the value of $100^2$ and $2^{100}$
$100^2=100 \times 100=10000$
$2^{100}=2^{10} \times 2^{10} \times 2^{10} \times 2^{10} \times 2^{10} \times 2^{10} \times 2^{10} \times 2^{10} \times 2^{10} \times 2^{10}$
$=1024 \times 1024 \times 1024 \times 1024 \times 1024 \times 1024 \times 1024 \times 1024 \times 1024 \times 1024, \text { is clearly greater than } 10000$
$\therefore 2^{100}>100^2$
$100^2=100 \times 100=10000$
$2^{100}=2^{10} \times 2^{10} \times 2^{10} \times 2^{10} \times 2^{10} \times 2^{10} \times 2^{10} \times 2^{10} \times 2^{10} \times 2^{10}$
$=1024 \times 1024 \times 1024 \times 1024 \times 1024 \times 1024 \times 1024 \times 1024 \times 1024 \times 1024, \text { is clearly greater than } 10000$
$\therefore 2^{100}>100^2$
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